I'd say that Discourse is an alternative, some people consider it good, but I personally don't like it.

What I like in PhpBB forums I joined is the organization of topics, usually hierarchical; balance of information density, not too high, not to low; good pagination that is fast to load; ctrl-f does what you expect: search in current page; theming that usually makes each forum look unique; profile and signature customization; no gamification of usage; and probably many other stuff I forgot.

Many of these things are personal and YMMV of course.